Related papers: A Parareal Algorithm with Spectral Coarse Solver
We propose a parareal based time parallelization scheme in the phase-space for the particle-in-Fourier (PIF) discretization of the Vlasov-Poisson system used in kinetic plasma simulations. We use PIF with a coarse tolerance for the…
We describe a simple algorithm for spectral graph sparsification, based on iterative computations of weighted spanners and uniform sampling. Leveraging the algorithms of Baswana and Sen for computing spanners, we obtain the first…
This paper focuses on efficient steady-state computations of induction machines. In particular, the periodic Parareal algorithm with initial-value coarse problem (PP-IC) is considered for acceleration of classical time-stepping simulations…
Solving multiscale diffusion problems is often computationally expensive due to the spatial and temporal discretization challenges arising from high-contrast coefficients. To address this issue, a partially explicit temporal splitting…
In this paper, we study a generalized finite element method for solving second-order elliptic partial differential equations with rough coefficients. The method uses local approximation spaces computed by solving eigenvalue problems on…
The parareal in time algorithm allows to perform parallel simulations of time dependent problems. This algorithm has been implemented on many types of time dependent problems with some success. Recent contributions have allowed to extend…
We describe a novel algorithm for solving general parametric (nonlinear) eigenvalue problems. Our method has two steps: first, high-accuracy solutions of non-parametric versions of the problem are gathered at some values of the parameters;…
The paper deals with the developing of the methodological backgrounds for the modeling and simulation of complex dynamical objects. Such backgrounds allow us to perform coordinate transformation and formulate the algorithm of its usage for…
We target time-dependent partial differential equations (PDEs) with heterogeneous coefficients in space and time. To tackle these problems, we construct reduced basis/ multiscale ansatz functions defined in space that can be combined with…
Recently, sparsity-based algorithms are proposed for super-resolution spectrum estimation. However, to achieve adequately high resolution in real-world signal analysis, the dictionary atoms have to be close to each other in frequency,…
This paper is concerned with the approximations of random dispersal operators/equations by nonlocal dispersal operators/equations. It first proves that the solutions of properly rescaled nonlocal dispersal initial-boundary value problems…
State-of-the-art methods for Convolutional Sparse Coding usually employ Fourier-domain solvers in order to speed up the convolution operators. However, this approach is not without shortcomings. For example, Fourier-domain representations…
In this paper, we study a class of set cover problems that satisfy a special property which we call the {\em small neighborhood cover} property. This class encompasses several well-studied problems including vertex cover, interval cover,…
This paper aims at an accurate and efficient computation of effective quantities, e.g., the homogenized coefficients for approximating the solutions to partial differential equations with oscillatory coefficients. Typical multiscale methods…
Efficient solutions of large-scale, ill-conditioned and indefinite algebraic equations are ubiquitously needed in numerous computational fields, including multiphysics simulations, machine learning, and data science. Because of their…
Discrete variational methods show excellent performance in numerical simulations of different mechanical systems. In this paper, we introduce an iterative procedure for the solution of discrete variational equations for boundary value…
We give a simple, fast algorithm for hyperparameter optimization inspired by techniques from the analysis of Boolean functions. We focus on the high-dimensional regime where the canonical example is training a neural network with a large…
The spectral risk has wide applications in machine learning, especially in real-world decision-making, where people are not only concerned with models' average performance. By assigning different weights to the losses of different sample…
This work revisits operator learning from a spectral perspective by introducing Polar Linear Algebra, a structured framework based on polar geometry that combines a linear radial component with a periodic angular component. Starting from…
Spectral algorithms leverage spectral regularization techniques to analyze and process data, providing a flexible framework for addressing supervised learning problems. To deepen our understanding of their performance in real-world…